Chapter 25: Current, Resistance and Electromotive...
Transcript of Chapter 25: Current, Resistance and Electromotive...
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Charge carrier motion in a conductor in two parts
Constant Acceleration
Randomizing Collisions (momentum, energy)=>Resulting Motion
Average motion = Drift Velocity = vd ~10-4 m/s
Typical speeds ~ 106 m/s
Chapter 25: Current, Resistance and Electromotive Force
F ma qE
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Current Flow = net motion of charges = Charge carriers
charge qspeed vd
I = Current = rate at which charge passes the area
vd
I dQdt
CS
Amp A units: 11
1 1
I
vd I
Negative charge carriers move in opposite direction of conventional current.
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Connection with microscopic picture:
vd
E
v dtd
A
q
I dQdt
nqv Ad
Current Density:J I
Anqv
J nqv
d
d
J n q v n q vd d 1 1 1 2 2 2
dQ = charge that passes through A= number that pass through A charge on each= (n A vd dt) q, n = number density = number/volume
(works for negative charge carriers, multiple types of charge carriers as well)
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Example: 18 gauge copper wire (~1.02 mm in diameter) -constant current of 2A-n = 8.5x1028 m-3 (property of copper)
find J, vd
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Current as a response to an applied electric field
J J EE
EJ
V mA m
VA
m m
( )
= conductivity
resistivity
units = =
1
2
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depends upon•material•E•Temperature
If does not depend on E, the material is said to obey “Ohm’s Law”
J
E
slope = 1/
linear responseOhm’s Law
J
E
nonlinear response
J
E
diodenonlinear response
direction dependence!
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For a cylindrical conductor
E J I
a b
E JV V E
J IA
R VI A
V IR
ab
resistance
Example: 50 meter length of 18 gauge copper wire (~1.02 mm in diameter) constant current of 2A = 1.72x10-8 .mfind E,V, R
see also example 28-3 re: alternate geometries
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Temperature Dependence of
TMetallic Conductor
TSuperconductor
TSemiconductor
T o o
T o o
T T
R R T T
[ ( )]
[ ( )]
1
1temperature coefficient of resistivity
For small changes in temperature:
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Resistor Color Codes
Color number color rangeblack 0 none ±20%brown 1 silver ±10%red 2 gold ±5%orange 3yellow 4 value: n1n2x10n3±x%green 5blue 6violet 7gray 8white 9 10x102±5%
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Electromotive Force and CircuitsSteady current
requires a complete circuitpath cannot be only resistance
cannot be only potential drops in direction of current flowElectromotive Force (EMF)
provides increase in potential converts some external form of energy into electrical energy
Single emf and a single resistor:
I
V = IR
+ - V = IR =
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Measurements
Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device.
V
Ammeters measure current through a device by being placed in series with the device.
A
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Real Sources and Internal Resistance
ra b
Ideal emf determined by how energy is converted into electrical energy
Internal Resistance r unavoidable “internal” lossesaging batteries => increasing internal resistance
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A
V
A
ra b
Open Circuit I=0Vr=0Vab=
ra b
Short Circuit Vr = Ir = Vab= 0
V
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A r
a b
Complete Circuit V
RI
IrVrR
I
IRIr
ab
ra b
Charging Battery
IIrVab V
A
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Energy and Power
V=IR
I + -a b
V=
+ -a b
ab
abab
IVdt
dWP
IdtVdQVdW
Resistance
P IV I R VR
22
battery +) of into ( or to +) ofout (by deliverdPower
emf Ideal
II
IP
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Power and Real Sources
ra b
Discharging BatteryI
rIIIVIrV
ab
ab2 :externally deliveredPower
I
ra b
Charging BatteryI
rIIIVIrV
ab
ab2 :source externalby deliveredPower
I
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RrPPeff
RrR
RIP
rrR
rIP
rRIP
RrrRRIRV
rRI
R
R
r
R
11
1
22
22
2
E
Real Battery with Load
I
A r
a b
V
R
max
"Impedance Matching"
PdPdR
R r
R
R 0
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Complete Circuit Example
A =12V r = 2
a b
V
R = 4
IVPPPP
ab
r
R
Vab
E
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Theory of Metallic ConductionConstant Acceleration between randomizing collisions
(momentum, velocity randomized)
EJ
J nqv
a Fm
qEm
v v a
v a qEm
v
J nqv nqm
E
mnq
d
o
avg d
d
2
2
E
mean time between collisions
mean free path= (
vo avg)
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Example: What is the mean time between collisions and the mean free path for conduction electrons in copper?
127 1085 109 1 10
16 10
1 10
8
28 3
31
19
6
.
..
.
mn mm kgq e C
v x mso
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Physiological Effects of Current
Nerve action involves electrical pulses
currents can interfere with nervous system
~.1A can interfere with essential functions
(heartbeat, e.g.)
currents can cause involuntary convulsive muscle action
~.01 A
Joule Heating (I2R)
With skin resistance
dry skin: R ~ 500k
wet skin: R ~ 1000